The present invention relates to a computerized method for simulating a high-viscosity fluid.
In recent years, there have been proposed various computerized simulation methods including such a method in which a flow state of a plastic fluid such as uncrosslinked rubber or resin composite which is knead in a camber of a mixer such as banbury mixer is computed or simulated by calculating Navier-stokes equation.    [patent document 1] JP-A-2011-27593    [non-patent document 1] “Numerical and Experimental study of Dispersive Mixing of Agglomerates” V. Collin, E. Peuvrel-Disdier et al.
In the case of a flow calculation for a low-viscosity fluid such as air, the flow velocity of the fluid may be set at zero on the surface of a wall of a space where the fluid flows. However, in the case of a flow calculation for a high-viscosity fluid such as an uncrosslinked rubber composite not yet vulcanized, on the surface of a wall of a space where the fluid flows, the fluid may have a certain value of the flow velocity in the flow direction. Thus, the fluid slips on the wall. When making a computerized simulation for such a high-viscosity fluid, such slip phenomenon on a wall has to be taken into consideration.
Heretofore, the fluid velocity on a wall surface (hereinafter, slip velocity) is defined by a function of a shear stress on the wall surface. When the slip velocity is linear, the shear stress TW in accordance with Navie's Law is given by the following equation (1):TW=Fslip[vslip−vwall]  (1)    and, when the slip velocity is nonlinear, the shear stress TW is given by the following equation (2):TW=Fslip[vslip−vwall]|vslip−vwall|eslip-1  (2)wherein    “vslip” is the velocity of the fluid on the wall surface in a direction parallel with the wall surface,    “vwall” is a component of the moving velocity of the wall surface in a direction parallel with the wall surface,    “Fslip” is a user-defined invariable, and    “eslip” is a user-defined invariable.
The value set to the invariable “Fslip” is specific to the fluid concerned and relates to the easiness of causing slip. Usually the value is determined through an experiment employing a device as disclosed in the patent document 1 for example. Through such experiment, the shear stress TW on a wall surface of a space in which the fluid flows, the slip velocity “vslip” on the wall surface, and the moving velocity“vwall” of the wall surface are measured.
Then, the value of “Fslip” is determined therefrom. More specifically, a double logarithmic chart, in which the slip velocity “vslip” is plotted on the x-axis and the shear stress TW is plotted on the Y-axis, is prepared, and then a power approximation curve to the plotted points is found asy=a·xb.
The “Fslip” and “eslip” are determined by the coefficient “a” and the power “b”, respectively.
Then, the slip velocity (vslip) on the wall surface is obtained by the following equation (3):vslip=vwall+TW/Fslip  (3)
The obtained slip velocity (vslip) is given to a solver, and according thereto, the solver performs a convergent calculation to obtain solution.
If the value of the invariable “Fslip” is small or the value of the shear stress TW is abnormal, then the value of the slip velocity “vslip” obtained from the equation (3) and given to the solver becomes abnormal.
Thus, if the slip velocity is introduced in the conventional fluid simulation method, there is a possibility that the computation becomes uncertain such that the iterative calculation is not converged or diverges.